Math 181.S96, Construction: The Circle's Rectangle
This construction is basic to the argument of Brunés'
The Secrets of Ancient Geometry.
ANIMATE:
The construction, animated at the rate of one frame per second.
THE STEPS: The construction, step-by-step.
- Step 01
: We begin with the end result of the construction
of the oriented square: a square with
its upright cross.
- Step 02
: Add the circle of the square.
This is the symbol "C" of Brunés.
- Step 03
: Draw the acute angle from the top of the cross
to the lower two corners of the square.
This is the symbol "O" of Brunés.
- Step 04
: Draw the acute angle from the bottom
of the cross to the upper corners of the
square.
This is the symbol "P" of Brunés.
- Step 05
: Draw the vertical straight line segment
determined by two of the crossings
of the acute angles and the circle of the square.
- Step 06
: Draw the other vertical line segment determined
by the acutes crossing the circle.
- Step 07
: The red rectangle is the rectangle of the circle
of the square.
The entire figure is the symbol "Q" of Brunés.
If you know the Pythagorean triple (1,2,sqrt 5),
it is not hard to see that the area of the circle's
rectangle is 80% of the area of the square, and
this approximates the area of the circle of
the square within 1.86%.
Ralph Abraham. Revised 17 April 1996.
